LMFDB - Dirichlet character orbit 19908.mt

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(19908, base_ring=CyclotomicField(78)) M = H._module chi = DirichletCharacter(H, M([39,65,52,16])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(95, 19908)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("19908.95"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$19908$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$19908$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$78$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{39})$
Fixed field:	Number field defined by a degree 78 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{19908}(95,\cdot)$	$1$	$1$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{19908}(1103,\cdot)$	$1$	$1$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{19908}(1859,\cdot)$	$1$	$1$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{19908}(2963,\cdot)$	$1$	$1$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{19908}(4631,\cdot)$	$1$	$1$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{19908}(5483,\cdot)$	$1$	$1$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{19908}(5891,\cdot)$	$1$	$1$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{19908}(7499,\cdot)$	$1$	$1$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{19908}(7751,\cdot)$	$1$	$1$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{19908}(9011,\cdot)$	$1$	$1$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{19908}(9767,\cdot)$	$1$	$1$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{19908}(10775,\cdot)$	$1$	$1$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{19908}(11183,\cdot)$	$1$	$1$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{19908}(12191,\cdot)$	$1$	$1$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{19908}(12791,\cdot)$	$1$	$1$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{19908}(13703,\cdot)$	$1$	$1$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{19908}(13955,\cdot)$	$1$	$1$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{19908}(14303,\cdot)$	$1$	$1$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{19908}(14459,\cdot)$	$1$	$1$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{19908}(14555,\cdot)$	$1$	$1$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{19908}(15971,\cdot)$	$1$	$1$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{19908}(17075,\cdot)$	$1$	$1$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{19908}(17327,\cdot)$	$1$	$1$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{19908}(18743,\cdot)$	$1$	$1$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{5}{13}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)
\(\chi_{19908}(95,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{19908}(1103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{19908}(1859,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{19908}(2963,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{19908}(4631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{19908}(5483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{19908}(5891,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{19908}(7499,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{19908}(7751,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{19908}(9011,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{19908}(9767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{19908}(10775,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{19908}(11183,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{19908}(12191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{19908}(12791,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{19908}(13703,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{19908}(13955,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{19908}(14303,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{19908}(14459,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{19908}(14555,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{19908}(15971,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{19908}(17075,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{19908}(17327,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{19908}(18743,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{5}{13}\right)\)

Introduction

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Properties

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Basic properties

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Characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	19908.mt
Modulus	$19908$
Conductor	$19908$
Order	$78$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(19908\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(19908\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(78\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);